Application of Blast-Pile Image Analysis in a Mine-to-Crusher Model to Minimize Overall Costs in a Large-Scale Open-Pit Mine in Brazil

Abstract

Amazon rainforests have many hidden treasures; thus, a balance between mine activities and the environment must be maintained. In the northern region of Brazil, there is a large diversity of metal ore deposits, the exploitation of which requires innovative and sustainable mining operations. Historically, mining operations have caused various environmental issues, such as landscape deterioration, damage to natural structures due to detonations, and soil and water pollution, and have also contributed to CO₂ emissions from diesel trucks. Here, to estimate and minimize the operating expenses of a large-scale open-pit iron mine, a mine-to-crusher model was developed. The calibration of the mine-to-crusher model was based on rock fragmentation from the blasting phase through the primary crushing phase from an analysis of pictures of the fragmented pile. A reduction in cost was determined for an optimum 90% passing size (P90). The calibration was performed with technical and economic parameters from 2 years before. For the studied iron ore mine site, an optimum P90 value between 0.29 and 0.31 m was determined.

1. Introduction

The understanding of productivity has a singular influence on mining production, as it is dependent on asset depletion, which focuses not only on grade decline but also on higher stripping ratios, complex mineralogy, and harder rock [1]. Mining operating costs can be higher now than before, as more compact ores are being mined now than they were years before [2]. Typically, mineral exploitation activities involve a comminution process that has a considerable effect on drilling, blasting, loading, hauling, and processing operations, and the costs associated with these activities can vary because of variations in rock fragment size across the entire process [3,4].

A mine-to-mill method considers the overall cost when optimizing mining costs; it tends to achieve a balance by investing in early processes to reduce later and costly processes. This means that minimum unit operational costs do not correspond to the minimum overall cost, and overall cost reduction can be achieved when all comminution operations are integrated [5]. The methodology can be interpreted in terms of the influence of reducing blasting costs on increasing excavation, haulage, and grid costs. This relationship between costs can be inversely influenced, as the greater the cost of drill and blasting is, the lower the subsequent process costs [6]. Smith; Faramarzi, and Poblete [7] considered that recognizing drilling and blasting as the first step in comminution can improve grinding capacity.

In work carried out by the Julius Krutschnitt Mineral Research Center (JKMRC) in Queensland, Australia, from 1996 to 2002, mathematical models and simulations were applied to improve mining and ore processing activities [8]. Ref. [9] provides a list of case studies from mine-to-mill applications, and Ref. [7] quotes studies that have shown an improvement in productivity from 5% to 20% [10,11,12,13,14]. Over the years, different authors have presented different approaches. For example, in [15,16,17,18], some scenario-based methods were proposed with practical applications for optimizing key performance indicators (KPIs). In [19], an approach involving an ore transportation model at the Aitik mine was contemplated when the impact of ore transportation time on mining costs was considered.

Since 2017, Navarro Torres et al. [20] have presented mathematical models that include the production chain from blasting to crushing/milling on the basis of the 80% passing size (P80) and validated these models for the different lithologies of Brazilian iron ore mines [4].

Hosseini et al. [21] considered the 80% passing size from the cumulative rock particle distribution as an essential and effective parameter to verify the quality of rock from haulage and crushing operations, as high equipment performance can be related to a smaller rock particle size. Moreover, some researchers have demonstrated how to predict rock particle size by evaluating blasting parameters [22,23]. Park et al. [24] and Manzoor et al. [25] considered analyzing drill monitoring for fragment prediction. Hosseini et al. [21] considered gene expression programming (GEP) via the Monte Carlo approach for predicting the rock particle distribution. Recent works have demonstrated effective improvements in the application of neural networks to predict blasting fragmentation [26,27,28,29,30].

As quoted by Navarro Torres et al. [4], Beyglou et al. [31] reported that, owing to large expenses on energy consumption, hard rock mines have been operated with pressure to reduce costs and optimize their operations. Considering this background, in this study, an economic-based model was applied and calibrated to predict and minimize costs for a large-scale open-pit iron ore mine in Brazil. Via this method, a correlation between the mine operational costs and the P90 fragment size obtained from the blast operation was revealed. A robust database was acquired containing economic and KPI values from unitary mine operations during the year 2022, which was subsequently processed and applied to the mathematical model. By focusing on higher blasting operational quality, the methodology of this work considers the P90 size rather than the usual P80 size to meet a high-quality criterion, as the mine lithologies are mainly friable rocks. Consider values above P90 would be exaggerated and more inaccurate if used.

2. Case Study

The study case was applied at an open-pit iron mine located at a mining complex in northern Brazil, which consists of a site using three loading faces that, in 2023, was planned to transport 22.3 million metric tons of ore and waste. The loading process starts with a Bucyrus 395 HR with a bucket capacity of 70 metric tons, a Komatsu PC8000 (75 metric tons) and a LeTourneau L-2350 GII (69 metric tons), where they operate together with different truck sizes, varying between Caterpillar CAT 793D, CAT 794 AC, CAT 797F e da Komatsu 830E AC, 930E-4, and 930E-4 AT. The primary crusher is a semi-mobile Metso C160 Jaw Crusher with a feed size under 1.20 m; the crushed ore is transported through a system of bench conveyors to the subsequent processes. The main types of iron-rich materials at the mine site are friable hematite, compact hematite, jaspillite, structural canga, chemical canga, and mafic rocks.

3. Materials and Methods

In this work, first, a survey was utilized to gather the mine site operating parameters and their costs from blasting to primary crushing. Subsequently, with the combination of equations that model an iteration from the operational costs and the technical parameters, a correlation was obtained between the overall cost and the P90 variation. The technical parameters and real costs of the process were acquired from a robust and complex database of information from the year 2023.

To achieve realistic modeling, all the parameters from each operation stage were processed, statically analyzed, and validated. The technical parameters from mine operations were estimated in two groups for the ore lithologies (friable and compact) and three groups for the waste lithologies (friable, semi-compact, and compact).

The correlation between the loading and hauling operations and the P90 particle size value was obtained from monitoring the blast parameters and the particle size distribution analysis from 3D photographs of the blasted piles. For this method, a 3D camera with software from the PortaMetrics device was used to determine the fragmentation curve for each analyzed blast.

In the final step, the overall costs for the mine phases were estimated and calibrated according to the rock fragmentation variability (P90). Finally, an optimal band size for each group between the ore and waste materials was obtained. The following sections present the detailed methods used.

3.1. Drill & Blast Operations

The quality during drilling and blasting operations can be measured by the particle size distribution of rock fragments; this fragmentation influences not only the cost of drilling and blasting but also the loading, transportation, and crushing operations [5,22,32]. As quoted in [4], an optimized particle size distribution can be obtained by varying the blast design parameters. Equation (1) shows how to determine the operating costs of drilling and blasting (Cdb), considering the P90 value. If we applied the P80 value, an adaptation over the Rosin Rammler method for determining the passing size value due to the X50 (50% material passing size) should be made, which would lead to a lower value multiplying the Rock factor on Equation (1).

$$C_{db}=[\left({\$}_d\left(H+J\right)+Q_{ex}{\$}_{ex}+{\$}_{ai}\right)/{\rho }_r] {\left({\displaystyle \frac{{3.32}^{1/n}{\mathrm{A}}_r}{P_{90}}}\right)}^{1.25}{\left({\displaystyle \frac{115}{RWS.{\mathrm{Q}}_{ex}}}\right)}^{0.8}$$

(1)

where ${\$}_d$ is the drilling cost per meter; H is the bench height (m); J is the stem length (m); $Q_{ex}$ is the explosive charge per hole (kg/hole); ${\$}_{ex}$ is the explosive cost; ${\$}_{ai}$ is the blasting accessories cost ($); ${\rho }_r$ is the rock density (t/m³); $A_r$ is the rock factor; $P_{90}$ is the 90% fragment passing size from blasting (cm); and RWS is the relative weight strength of the explosive as a function of ANFO (%).

3.2. Loading Operations

The load and haul operation in the open-pit mine design has the principle of truck-shovel matching, which selects the best truck model according to the shovel capacity. This matching can be determined by the bucket-to-capacity ratio, which is based on the capacity of the truck compartment and the shovel’s bucket volume, and the best matching is achieved when the bucket-to-capacity ratio allows the system’s maximum working efficiency to be reached [33,34,35,36].

The system’s maximum working efficiency involves the full utilization of the bucket volume, which depends on the particle size distribution and particle lumpiness resulting from blasting. To determine the relationship between fragment size and loading efficiency, the dig time, which is the most sensitive part to vary due to muck pile characteristics [37], is analyzed. In a previous study, Navarro Torres et al. [4] used the Jethro and Shehu [38] experimental model to calibrate the dig time as a function of the P80 value via Equation (2). The model obtained from Jethro and Shehu’s work [38] showed that the exponential function could achieve a better representation of the relationship between fragment size and loading efficiency, where the a coefficient represents lithology conditions, load equipment operator ability, and equipment conditions:

$$t_e=a\left({exp}^{0.05P_{80}}\right)$$

(2)

where $t_e$ is the excavation/dig time (s) and $a$ is a constant determined from a regression analysis between the dig time and fragment size from loading operations.

However, a new method was applied to this calibration by using the direct equation obtained from a regression analysis between the dig time and the P90 fragment size from blasting, by using P90 values rather than P80, we will obtain a higher value for the constant a so the cost variation on the equations involving Load and Haulage operations can be adapted to the new consideration. This was possible by using an intelligent 3D camera system for fragmentation analysis, namely, the PortaMetrics camera. Three equations were obtained for three lithology groups: the friable lithology Equation (3) and the compact lithology Equation (4):

$$t_e=9.5192\left({exp}^{0.02P_{90}}\right)$$

(3)

$$t_e=11.317\left({exp}^{0.017P_{90}}\right)$$

(4)

To determine the costs for loading operations (Cl), Equation (5) shows how to measure the function P90 and the equations for excavation time above as follows:

$$C_l={\displaystyle \frac{{\$}_l\left[t_e\left(equation\right)+{2t}_i+t_d\right]}{3600U_c{L}_c}}$$

(5)

where ${\$}_l$ is the hourly cost for loading operation ($/h), $t_e$ is the equation for each lithology, $t_i$ is the time for the loading equipment to move between the muck pile and the truck (s), $t_d$ is the dumping time (s), $U_c$ is the loading equipment utilization (%), and $L_c$ is the equipment payload (t).

3.3. Haulage Operations

As quoted in the previous section, optimization of a load and haul operation depends on loading-hauling equipment matching, which depends on the models of both types of equipment. For this study case, there are three loading equipment models with two approximate bucket capacities (75 tons and 70 tons) and six hauling equipment models with two approximate capacities (240 tons and 340 tons), where their operation does not work in a matching regime. The actual operation works over the offer and demand for trucks, which means that it will use the available truck for the available loading equipment.

By far, this is an issue for modeling, as the cost estimation for both operations (loading and haulage) is also determined by the equipment capacity. To achieve the best case, different scenarios were simulated considering the two groups of trucks and their different capacities by determining which matching was the best option for general cost optimization.

For the hauling operation cost (Ch), Equation (6) shows how to measure the P90 value:

$$C_h={\displaystyle \frac{{\$}_h\left[\left[\left(t_e\left(equation\right)+2t_i+t_d\right)/60\right]p+(t_t+t_{td}+t_{te})\right] }{60U_h{L}_h}}$$

(6)

where ${\$}_h$ is the hourly cost for the hauling operation ($/h), $t_e$ is the equation for each lithology, $t_i$ is the time for the loading equipment to move between the muck pile and the truck (min), $t_{td}$ is the truck dumping time (min), $t_t$ is the truck travel cycle time (min), $t_{te}$ is the truck waiting time (min), $U_h$ is the hauling equipment utilization (%), and $L_h$ is the truck capacity (t).

3.4. Primary Crushing Operations

In Navarro Torres et al. [4], previous studies that aim to define crushing capacity through the crusher type are suggested [39,40]. When considering the jaw crusher presented in the study case, the crusher nominal capacity as a function of the P90 value can be determined by (Ppc_P90) Equation (7):

$$P_{pc\_P90}=P_{pc}{e}^{-0.002F90}$$

(7)

where $P_{pc}$ is the primary crusher nominal production capacity (t/h) and F90 is the 90% particle size feed at the primary crusher.

Then, the cost of primary crushing operations can be determined by (Cpc) Equation (8) as a function of the P90 value. If applied to the P80 value, it would obtain a higher crushing capacity, which would lead to a lower primary crushing operating cost.

$$C_{pc}={10W}_i\left({\displaystyle \frac{1}{\sqrt{P_{90}}}}-{\displaystyle \frac{1}{\sqrt{F_{90}}}}\right){\$}_{en}+{\displaystyle \frac{{\$}_{pc}}{f\left(P_{pc}{e}^{-0.002F_{90}}\right)}}$$

(8)

where $W_i$ is the work index (kWh/t), P90 is the 90% particle passing size from the crusher, ${\$}_{en}$ is the electric energy cost ($/kWh), and $f$ is the mineral mass fraction that will be crushed in the process.

4. Discussion

Model calibration is an important task for future estimates. To accomplish this, it was necessary to characterize the mine’s real costs by consolidating mine operating costs from 2022, as represented in

Table 1. Mining operational costs.

Mining Phase	USD/t	%
Mine Support	$0.10	4%
Infrastructure	$0.46	17%
Drill & Blasting	$0.35	13%
Loading	$0.27	10%
Hauling	$1.17	43%
Primary crushing	$0.34	13%
Total	$2.69	100%

and Figure 1.

Table 1 shows the overall mining operation cost, which totals 2.69 dollars a ton; however, it includes stages that are not directly related to the rock fragment size, which is the mine support and infrastructure costs. Therefore, it is necessary to not consider this cost before calibrating the model for cost minimization in this work, which makes the total cost reach 2.13 dollars a ton However, after the calibration is complete, it is possible to add this cost if desired.

When the cost distribution is considered, it is possible to determine the greatest influence of the hauling process on the overall cost, as it represents 43% of the total cost. In addition, if mine support and infrastructure are not considered, this percentage increases to 55% of the total mining unity cost. This shows that the hauling operations are the most critical operation influenced by the fragment size during the drilling to primary griding phase and that it has strong importance when trying to apply a cost reduction method.

As shown in Figure 1, the costs were determined by the time of production. To associate the production cost with the P90 value from the blasting phase, 3D pictures (Figure 2) from the muck pile for different lithologies and blasting parameters were analyzed with the equipment Portametrics, where the fragment sizes could be estimated by photos taken by the three external cameras from the Portametrics equipment which are able to determine the distance between the camera and the fragments as it software do an automatic image processing. The fragment distribution was produced for each of the studied lithologies by the camera software, which considers the larger size of the fragment to determine its area, different from other manual image processing, which defines the rock size by an equivalent diameter size from the fragment picture.

When the mine-to-crush process is considered, it is clear that not all the mine lithologies will pass through the whole process. Crushing will only be part of the process of ore lithology, and lithologies classified as waste will not be considered in this part of the study. The ore lithologies were considered to be another classification and were divided into friable and compact ores; friable ores were considered friable hematite, and compact lithologies were considered compact hematite and jaspelite.

These two groups of iron ore lithologies were correlated with the variation in the blasting P90 size and the dig/excavation time from the loading phase, where each image obtained from the Portametrics device was associated with the referred excavation time monitored when the photos were taken. With this process, it was possible to obtain Equations (3) and (4), which are graphically represented in Figure 3. However, there is uncertainty in this method, which is mainly related to sampling uncertainty as it was not possible to get pictures from all the pile volume, especially when the loading equipment could not stop at the time between loadings so the camera operator could get closer to the muck pile to take a photo.

On the basis of the interaction between Equations (1) and (8), the overall unitary cost for the mine-to-crush operations was determined via the technical and economic parameters of the mine site. However, as previously described, there is no optimum configuration for the load and haulage system, which means that the mine does not apply a shovel-truck matching to achieve the best loading time and productivity. As the truck capacity has a great influence on the productive costs, the model was calibrated for the two truck groups as described in Section 3.2. The key parameters for the friable and compact materials are shown in

Table 2. Mean parameters used for model calibration (240 t Trucks | 350 t Trucks).

Operation	Parameter	Friable	Compact
Drilling & Blasting	Drilling cost per meter ($d) (US$/m)	17.78	17.78
	Bench height (H) (m)	15	14
	Subdrill (J) (m)	1	1
	Explosive charge per hole (Qex) (kg/hole)	580	733
	Explosive cost ($ex) (US$/kg)	0.95	0.95
	Blasting accessories cost ($ai) (US$)	52.67	52.67
	Rock factor (Ar)	3	5
	Relative weight strength of the explosive (RWS) (%)	99	99
	Uniformity coefficient (n)	1.15	0.94
	Rock density (ρr) (t/m3)	3.27	3.09
Loading	Hourly loading cost ($l) ($/h)	1099.42	924.95
	Moving time (ti) (s)	6.77	8.25
	Dumping time (td) (s)	5.97	6.68
	Payload (Lc) (t)	61.2	61.49
	Utilization (Uc) (%)	1	1
Hauling	Hourly hauling cost ($h) ($/h)	698.26 | 1036.01	677.4 | 912.84
	Truck capacity (Lh) (t)	237.61 | 342.78	236.7 | 311.15
	Number of paces for full loading the truck (p)	4 | 6	4 | 6
	Travel time cycle (tt) (min)	12.22 | 13.07	12.94 | 13.42
	Truck Dumping time (ttd) (min)	1.29 | 1.14	1.16 | 1.04
	Truck waiting time (tte) (min)	7.63 | 7.78	7.73 | 7.83
	Utilization (Uh) (%)	1	1
Primary Crushing	Hourly cost for primary crushing operation ($pc) ($/h)	1209.6	1209.6
	Work Index (Wi) (KWh/t)	13.52	21.19
	90% particle passing size from the crusher (P90) (mm)	61	61
	Primary crusher nominal production capacity (Pbp) (t/h)	3546.75	3546.75
	Electric energy cost ($en) ($/KWh)	0.04	0.04

.

Finally, applying the obtained data (Table 2), the model was calibrated for the mine site at the Carajás Complex, and the cost reduction model was obtained for each lithology group (friable and compact) by varying the unitary costs as a function of the size of the rock fragment P90.

4.1. Cost Minimization Estimation

The results for friable and compact ores are shown in Figure 4. Figure 4a,b show the cost variation in each phase using the 240 t trucks, and Figure 4c,d show the cost variation in each phase using the 350 t trucks.

As shown in Figure 4a,b, friable materials achieved a minimum total cost of 1.92 USD/t and a compact cost equal to 1.96 USD/t. This is because the unitary mine cost value of 2.13 does not vary as a function of the type of material and its resistance. That is, a P90 value between 29 and 31 cm can achieve a cost reduction of 0.17 to 0.21 USD/t if trucks with a 240 t capacity are used. When considering trucks with higher capacity, the values increase to 2.06 USD/t for friable materials and 2.09 USD/t for compact materials, as shown in Figure 4c,d, achieving a cost reduction of 0.04 to 0.07 USD/t at a P90 fragment size ranging from 25 to 31 cm.

It is likely that an optimum P90 size for actual mine operation can be found in the range from 29 to 31 cm, as it is the common range between the models of both friable, compact, and all the truck capacities, achieving a cost reduction between 0.04 and 0.21 USD/t.

In addition, when comparing the types of lithologies, the minimum cost for friable materials was lower than that for compact materials. This can be related to the behavior of the drill and blasting curve, which is positioned higher for compact materials. This is because compact rocks need more explosive energy to fragment as they have a higher resistance. This means a higher cost for drilling and blasting operations.

4.2. Equipment Matching

Considering that the difference between the results for the different truck capacities is notable, for the loading equipment applied at the mine site, the best match would be for the smallest trucks (240 t average). This is because the difference between values is approximately 0.13 USD/t less for the small trucks than for the 350 t average capacity truck models.

Interestingly, more profitable operations with larger trucks are usually expected, but in this case, the cost for a hauling operation is greater. This can be explained by the slower average velocity of the 350 t trucks at full capacity, increasing their gas consumption. Table 2 also shows greater waiting and loading times for the 350 t trucks; this condition is explained by the greater number of loading cycles that loading equipment needs to perform to fill these trucks. Usually, production is expected to be increased by moving more material, but this model shows that the gain is unlikely to be beneficial for the studied mine site operation.

5. Conclusions

The mine-to-crusher model is a great tool for measuring the overall production cost, indicating the importance of considering the mining process as a whole and not segregating it by each phase. As a result, it is possible to gain a better understanding of each process and its influence on the larger scenario. Investing more in some processes can generate lower costs in subsequent processes, such as investing in better drill and blast operations to achieve a lower cost of primary crushing.

In this study case, a P90 ideal fragment size between 29 cm and 31 cm was achieved for any lithology from the studied mine site. This also shows that it is highly important to have a good configuration between loading and hauling equipment, as having larger equipment does not always result in more profitable operations.